Volumetric expansion coefficients of simple materials are often well cataloged. however, the thermal expansion coefficient β of a human body is less well known. this could affect the human body's specific gravity and, therefore, measurements of its body‑fat ratio. suppose that a human body of weight w0 on dry land is placed on a scale while completely immersed in formaldehyde of temperature t1. once the temperature increases by, δt, the scale reading drops by δw. derive an expression for β in terms of δt, w0, and δw by assuming that the ratio of the density of formaldehyde rhof and the initial density of the body rhob is r=rhof/rhob. assume also that rhof does not change when heated.